Download Magnetic fields in Local Group dwarf irregulars⋆

Astronomy
&
Astrophysics
A&A 529, A94 (2011)
DOI: 10.1051/0004-6361/201015393
c ESO 2011
Magnetic fields in Local Group dwarf irregulars
K. T. Chyży1 , M. Weżgowiec1,3 , R. Beck2 , and D. J. Bomans3
1
2
3
Obserwatorium Astronomiczne Uniwersytetu Jagiellońskiego, ul. Orla 171, 30-244 Kraków, Poland
e-mail: [email protected]
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
Received 14 July 2010 / Accepted 24 January 2011
ABSTRACT
Aims. We wish to clarify whether strong magnetic fields can be effectively generated in typically low-mass dwarf galaxies and to
assess the role of dwarf galaxies in the magnetization of the Universe.
Methods. We performed a search for radio emission and magnetic fields in an unbiased sample of 12 Local Group (LG) irregular
and dwarf irregular galaxies with the 100-m Effelsberg telescope at 2.64 GHz. Three galaxies were detected. A higher frequency
(4.85 GHz) was used to search for polarized emission in five dwarfs that are the most luminous ones in the infrared domain, of which
three were detected.
Results. Magnetic fields in LG dwarfs are weak, with a mean value of the total field strength of <4.2 ± 1.8 μG, three times lower than
in the normal spirals. The strongest field among all LG dwarfs of 10 μG (at 2.64 GHz) is observed in the starburst dwarf IC 10. The
production of total magnetic fields in dwarf systems appears to be regulated mainly by the star-formation surface density (with the
power-law exponent of 0.30 ± 0.04) or by the gas surface density (with the exponent 0.47 ± 0.09). In addition, we find systematically
stronger fields in objects of higher global star-formation rate. The dwarf galaxies follow a similar far-infrared relationship (with a
slope of 0.91 ± 0.08) to that determined for high surface brightness spiral galaxies. The magnetic field strength in dwarf galaxies
does not correlate with their maximum rotational velocity, indicating that a small-scale rather than a large-scale dynamo process is
responsible for producting magnetic fields in dwarfs. If magnetization of the Universe by galactic outflows is coeval with its metal
enrichment, we show that more massive objects (such as Lyman break galaxies) can efficiently magnetize the intergalactic medium
with a magnetic field strength of about 0.8 nG out to a distance of 160–530 kpc at redshifts 5–3, respectively. Magnetic fields that
are several times weaker and shorter magnetization distances are expected for primordial dwarf galaxies. We also predict that most
star-forming local dwarfs might have magnetized their surroundings up to a field strength about 0.1 μG within about a 5 kpc distance.
Conclusions. Strong magnetic fields (>6 μG) are observed only in dwarfs of extreme characteristics (e.g. NGC 4449, NGC 1569, and
the LG dwarf IC 10). They are all starbursts and more evolved objects of statistically much higher metallicity and global star-formation
rate than the majority of the LG dwarf population. Typical LG dwarfs are unsuitable objects for the efficient supply of magnetic fields
to the intergalactic medium.
Key words. galaxies: evolution – galaxies: magnetic fields – galaxies: dwarf – galaxies: irregular – Local Group – radio continuum:
galaxies
1. Introduction
Dwarf galaxies are the most numerous population of galaxies
in the Universe (Grebel 2001) and according to the hierarchical clustering scenario, they were the primary building blocks
of more massive galaxies in the past. They play a key role
in one of the most puzzling problems in the ΛCDM picture
of galaxy formation, namely the “missing satellites problem”
(e.g. Kravtsov 2010). Much effort has been made to understand the origin of star formation bursts, as well as the formation of filamentary structures in dwarfs (Hunter 2002; Hunter
& Gallagher 1990). In contrarast to the massive spiral galaxies,
the star formation activity in dwarfs occurs without any strong
influence from density waves (Hunter et al. 1998) and usually
develops stochastically.
Magnetic fields can bee especially important in these lowmass galaxies because of their lower gravitational potential and
Based on observations with the 100-m telescope at Effelsberg operated by the Max-Planck-Institut für Radioastronomie (MPIfR) on behalf
of the Max-Planck-Gesellschaft.
the greater ability of their gas to escape via galactic winds.
These fields enable magnetic fields to be supplied to the intergalactic medium (IGM) at early cosmological epochs (Kronberg
et al. 1999; Bertone et al. 2006). However, the generation of
magnetic fields in dwarf galaxies by a classical large-scale dynamo can be inefficient because of the slow or chaotic rotation and hence low differential rotation of these galaxies
(Chyży et al. 2003). Star formation activity would produce
magnetic fields by generating a small-scale dynamo (Zeldovich
et al. 1990), but the magnetic fields and star formation would
then be related in a nonlinear way (Chyży 2008). Thus, it is unclear whether strong magnetic fields could be effectively generated in these low-mass galaxies and under stochastically generated star formation the large-scale structures of magnetic fields
could be developed.
Surprisingly, very strong magnetic fields were discovered in
the optically bright dwarf irregular galaxy NGC 4449, with the
total field intensity of about 12 μG and a regular component of
up to 8 μG (Chyży et al. 2000). Similar fields were detected
in NGC 1569 (Kepley et al. 2010). Weaker total fields, in the
range of 5−7 μG, were also observed in some other dwarfs as
Article published by EDP Sciences
A94, page 1 of 15
A&A 529, A94 (2011)
Table 1. Basic properties of the observed LG dwarfs∗ .
Galaxy
Name
Aquarius
GR 8
IC 1613
NGC 6822
WLM
IC 10
LGS 3
SagDIG
Sextans A
Sextans B
Leo A
Pegasus
Other
Name
DDO 210
DDO 155
DDO 8
DDO 209
DDO 221
UGC 192
PGC 3792
PGC 63287
DDO 75
DDO 70
DDO 69
DDO216
Type
dIrr
dIrr
Irr
Irr
Irr
Irr
dIrr/dSph
dIrr
dIrr
dIrr
dIrr
dIrr/dSph
Optical position
α2000
δ2000
20h 46m 51.s 8
−12◦ 50 52. 5
+14◦ 13 02. 9
12h 58m 40.s 4
+02◦ 07 04. 0
01h 04m 47.s 8
−14◦ 47 21. 4
19h 44m 56.s 6
−15◦ 27 39. 3
00h 01m 58.s 2
h
m s
+59◦ 18 13. 6
00 20 17.3
+21◦ 53 06. 0
01h 03m 55.s 0
h
m s
−17◦ 40 41. 3
19 30 00.0
−04◦ 41 34. 0
10h 11m 00.s 8
+05◦ 19 56. 0
10h 00m 00.s 1
h
m s
+30◦ 44 47. 0
09 59 26.5
+14◦ 44 34. 5
23h 28m 36.s 3
Apparent
size [ ]
2.2 × 1.1
1.1 × 1
16.2 × 14.5
15.5 × 13.5
11.5 × 4
6.8 × 5.9
2×2
2.9 × 2.1
5.9 × 4.9
5.1 × 3.5
5.1 × 3.1
5 × 2.7
Linear
size [kpc]
0.61 × 0.30
0.70 × 0.64
3.44 × 3.08
2.25 × 1.96
3.08 × 1.07
1.31 × 1.13
0.36 × 0.36
0.88 × 0.64
2.26 × 1.88
2.02 × 1.39
1.03 × 0.62
1.11 × 0.60
Distance
[kpc]
940
2200
730
500
920
660
620
1040
1320
1360
690
760
Notes. (∗) Data from Mateo (1998); Karachentsev (2005); and the NED database.
NGC 6822 (Chyży et al. 2003), IC 10 (Chyży et al. 2003), and
the Large Magellanic Cloud (LMC: Gaensler et al. 2005). In the
Small Magellanic Cloud (SMC), a weak total field of about 3 μG
was found, partly on large-scales (Mao et al. 2008). Since all
these galaxies are optically bright and nearby objects, the detection of magnetic fields in them may be influenced by strong
selection effects. The question then arises of whether they represent a typical sample of dwarf galaxies and the typical conditions
for dynamo processes to occur.
To date, there has been no systematic study of diffuse nonthermal radio emission and polarization in a uniformly selected
sample of dwarf galaxies with diverse star formation activities,
kinematics, masses, and gas contents. One ideal target for such
an investigation is the Local Group (LG), which contains a mixture of small irregular and dwarf galaxies around two giant spirals. Many dwarfs in the Local Group are star-forming objects
(Mateo 1998) with a wide range of star-forming activity (Hunter
& Elmegreen 2004; Dolphin et al. 2005; Tolstoy et al. 2009).
As a complete sample of local galaxies, LG dwarfs can be studied to provide reliable statistical insight into association of magnetic fields with other galactic properties. They also provide a
unique opportunity to investigate the relationship between magnetic fields in dwarfs and those in larger stellar systems, giving
valuable estimates of the efficiency of galactic dynamo processes
working in low-mass objects.
In this paper, we report the results of a systematic attempt to
detect diffuse radio emission and magnetic fields in LG irregular and dwarf irregular galaxies. This sensitive study was conducted with the 100-m Effelsberg radio telescope at 4.85 GHz
and 2.64 GHz. In the next section, we describe the criteria used
to build our sample of dwarf galaxies and in Sect. 3 provide details of the observations and data reduction process. The radio
maps, derived radio emission fluxes, and estimates of magnetic
field strengths are presented in Sect. 4. In Sect. 5 we investigate
how magnetic fields might possibly be influenced by the global
and local star formation rate, galactic mass, rotation, metallicity,
and star formation history. We also investigate the possibility
of the Universe being magnetized by outflows from dwarfs using our current knowledge on the IGM metal enrichment. We
then discuss the prevalence of large-scale magnetic fields in
dwarfs, and construct a radio-infrared diagram to check whether
dwarfs deviate from the general correlation trend followed by
optically bright spiral galaxies. We summarize our studies in
Sect. 6.
A94, page 2 of 15
2. The sample
The Local Group consists of about 41 members, the most massive and optically bright of which are the three spiral systems the
Milky Way, the M 31, and the small M 33. Less significant members include seven galaxies of irregular type (Irr), e.g., LMC,
and 31 dwarfs. A subgroup of 14 dwarfs, called dwarf irregulars
(dIrr), are low-mass objects (M ≤ 109 M ) but like irregulars are
gas-rich and display evidence of current or recent star formation
(Mateo 1998; Tolstoy et al. 2009). The remaining 31 dwarfs,
known as dwarf ellipticals (dE) and dwarf spheroidals (dSph),
are prime examples of gas-poor systems dominated by old stellar populations, that show no signs of current star formation.
They are low-luminosity (MV ≥ −14 mag), strongly dark-matter
dominated systems, with total masses of about 107 M (Strigari
et al. 2008). Although dSphs experienced star formation over
extended time intervals in their youth, today all of them but one
appear to be completely free of detectable interstellar material
(Grebel et al. 2003). A new population of ultrafaint dSphs (UF
dSphs) with absolute magnitude MV ≥ −6 were observed by
Martin et al. (2008). They are more metal-poor than dSphs, their
more luminous counterparts. Ursa Minor and Draco are examples of these systems, whose stellar velocity dispersions are only
a few kilometres per second, and whose total masses of less than
106 M are composed primarily of very old stars.
For our systematic search for radio emission and magnetic
fields, only gas-rich systems that display evidence of star formation activity, hence irregular and dwarf irregular galaxies, are
suitable. Following Mateo (1998), we do not distinguish between these two types of objects and call them hereafter dwarf
irregular galaxies.
There are in total 12 LG dwarf irregular galaxies of declination larger than about −25◦ , and thus available for radio observations from the site of the 100-m Effelsberg telescope. The
details of the sample are presented in Table 1. To detect their
radio emission and achieve an adequate balance between resolution and sensitivity we used the 2.64 GHz (11 cm) receiver of
the Effelsberg telescope. Using a relatively low frequency, we
also minimized the contribution of radio thermal emission. At
this frequency, the telescope beam size of 4. 6 is still sufficient
to probe the large-scale radio emission of LG dwarfs, which are
often of large angular size (up to 19 ; Table 1). Radio interferometers that could provide data of higher resolution are inappropriate for observations of these large and diffuse objects.
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
Table 2. Parameters of the radio observations of all galaxies studied at 2.64 GHz.
Galaxy
Aquarius
GR 8
IC 1613
NGC 6822
WLM
IC 10
LGS 3
SagDIG
Sextans A
Sextans B
Leo A
Pegasus
Map size
arcmin × arcmin
30 × 30
30 × 30
44 × 44
44 × 44
40 × 40
36 × 36
30 × 30
30 × 30
40 × 40
40 × 40
40 × 40
40 × 40
rms in final map
mJy/b.a.
0.77
0.54
1.10
1.20
1.40
3.90
0.49
0.72
1.70
1.10
0.88
0.81
For a selected subgroup of 5 out of 12 dwarfs with a high
star-formation rate (SFR) (see Table 3), we also attempted to
investigate in addition radio polarized emission at 4.85 GHz
(6.2 cm). We had observed three galaxies, NGC 6822, IC 10
(Chyży et al. 2003), and IC 1613 before with the Effelsberg telescope. For the remaining two galaxies, Sextans A and Sextans B,
we carried out separate observations at 4.85 GHz.
3. Observations and data reduction
The Effelsberg observations were made in May 2007 (Table 2).
The unbiased sample of 12 LG dwarfs were observed at
2.64 GHz using a single horn receiver. We scanned our objects
alternatively along the RA and Dec directions. The subgroup
of two galaxies mentioned above were additionally observed at
4.85 GHz using a two-horn (with horn separation of 8 ) system in the secondary focus of the radio telescope (see Gioia
et al. 1982). The coverages were obtained in this case in the
azimuth-elevation frame. At both frequencies, the horns were
equipped with two total-power receivers and an IF-polarimeter,
resulting in four channels containing the Stokes parameters I
(two channels), Q, and U. The telescope pointing was corrected
by repeating cross-scans of a bright point source close to the observed galaxy at time intervals of about 1.5 h. The flux density
scale was established by mapping the calibration sources 3C 138
and 3C 286. Table 2 presents the details of our observations at
2.64 GHz.
The data reduction was accomplished using the NOD2 data
reduction package (Haslam 1974). At 2.64 GHz, the obtained
coverages in I, Q, and U channels (from a single horn system)
were combined using the spatial-frequency weighting method
(Emerson & Gräve 1988), followed by a digital filtering process that removed the spatial frequencies corresponding to noisy
structures smaller than the telescope beam.
At 4.85 GHz (dual system used), we combined the data from
the two horns, using the “software beam switching” technique
(Morsi & Reich 1986), followed by restoration of total intensity
channel I (Emerson et al. 1979). We then combined I, Q, and
U maps using the same procedure as for 2.64 GHz and obtained
the final maps of total power, polarized intensity, polarization
degree, and polarization position angles.
4. Results
4.1. Radio detections
Among the 12 observed LG dwarfs, we clearly detected extended radio emission at 2.64 GHz in three cases: IC 10,
No. if coverages
8
15
11
8
11
10
10
10
18
12
8
12
Total flux
mJy
≤1.2
≤0.8
17 ± 2
120 ± 20
≤4.2
250 ± 20
≤0.74
≤1.1
≤2.6
≤1.7
≤1.3
≤1.2
NGC 6822, and IC 1613. To estimate their radio fluxes reliably
or their upper limits in cases of no detection the emission from
confusing background sources had to be removed. For identification of background sources, we compared our radio maps with
those of the Condon (1987), NVSS1 , and FIRST2 surveys. We
then applied the “subtraction” method (Chyży et al. 2003) and
removed all confusing sources from the maps. For clear detections of dwarfs their total fluxes were obtained by integrating the
signal in polygonal areas encompassing all visible radio emission. If there was no detection, we defined the upper limit of
flux density as 1.5 times the rms noise level of the map multiplied by the number of beams covering the optical extent of a
given galaxy. These estimates are presented in Table. 2. All the
detected galaxies are presented below and in Figs. 1–5, which
also show background sources. Polarized emission was detected
in NGC 6822, IC 10 (Chyży et al. 2003), and IC 1613 (Figs. 4, 5)
all at 4.85 GHz. To show the structure of the magnetic field projected on the sky plane, we used the apparent B-vectors defined
as E-vectors rotated by 90◦ . Faraday rotation was expected to be
small at 4.85 GHz.
IC 10. – The map of total intensity at 2.64 GHz (Fig. 1)
clearly detects, slightly resolved, and elongated radio emission.
It appears to be the strongest (250 mJy) source in our sample.
The small extension to the west is caused by a weak (9 mJy)
background source, also visible in the NVSS map at 1.4 GHz.
The emission is fully compatible with the 10.45 GHz map of
Chyży et al. (2003). The spectral index between both frequencies is about 0.35 ± 0.05, which is in good agreement with
Klein & Gräve (1986). IC 10 is experiencing a massive starburst, apparently triggered by infalling H i gas from the southeast
(Grebel 2004). The synchrotron emission detected in this portion
of the galaxy indicates gas compression (Chyży et al. 2003).
According to several authors (see Grebel 2004 and references
therein), the properties of this galaxy suggest that it should be
classified as a blue compact dwarf.
NGC 6822. – This galaxy has a three times lower total
star formation rate (based on Hα observations) than IC 10
(Woo et al. 2008), but contains several well-defined supernovae remnants and star-forming clumps (Chyży et al. 2003;
see also Table 3). Our radio map of the total intensity of NGC 6822 at 2.64 GHz (Fig. 2) shows significant
radio emission from this galaxy mainly associated with
distinct Hα regions. The emission peaks at the positions RA2000 = 19h 45m 40s , Dec2000 = −14◦ 34 , RA = 19h 45m 10s ,
1
NVSS: the NRAO VLA Sky Survey at 1.4 GHz, Condon
et al. (1998).
2
FIRST: Faint Images of the Radio Sky at 20 cm, Becker et al. (1995).
A94, page 3 of 15
A&A 529, A94 (2011)
IC 10 Effelsberg 2.64 GHz TP on DSS blue
IC 1613 Effelsberg 2.64 GHz TP on DSS blue
02 18
59 26
16
24
14
DECLINATION (J2000)
DECLINATION (J2000)
22
20
18
12
10
08
06
04
16
02
14
00
12
01 58
01 05 30
10
00 21 15
00
20 45
30
15
00 19 45
RIGHT ASCENSION (J2000)
30
15
Fig. 1. The total power map of IC 10 at 2.64 GHz overlaid onto the DSS
blue image. The contours are at 3, 5, 8, 16, 25, 40 × 3.9 mJy/b.a. The
map resolution is 4. 6. The beam size is shown in the bottom right corner
of the figure.
NGC 6822 Effelsberg 2.64 GHz TP on DSS blue
-14 35
DECLINATION (J2000)
40
45
50
55
-15 00
19 45 45
30
15
00
44 45
RIGHT ASCENSION (J2000)
30
15
Fig. 2. The total power map of NGC 6822 at 2.64 GHz overlaid onto
the DSS blue image. The contours are at 3, 5, 8, 15, 20, 40, 80 ×
1.2 mJy/b.a. The map resolution is 4. 6. The beam size is shown in the
bottom right corner of the figure.
Dec = −14◦ 37 , and RA = 19h 45m 15s , Dec = −14◦ 52 as well as
the extension to the south are due to background sources. The
overall distribution of radio emission corresponds well with our
earlier observations at 4.85 GHz (Chyży et al. 2003).
IC 1613. – This galaxy seems to be a typical LSB Irr evolving slowly in isolation without large bursts of star formation during its entire lifetime (Skillman et al. 2003). The total power
map at 2.64 GHz (Fig. 3) reveals radio emission mainly from
areas associated with two distinct Hα regions. The emission
A94, page 4 of 15
15
00
04 45
30
RIGHT ASCENSION (J2000)
15
Fig. 3. The total power map of IC 1613 at 2.64 GHz overlaid onto the
DSS blue image. The contours are at 3, 5, 8, 20, 40 × 1.1 mJy/b.a. The
map resolution is 4. 6. The beam size is shown in the bottom left corner
of the figure.
peaks at RA = 01h 04m 50s , Dec = 02◦ 04 and RA = 01h 04m 25s ,
Dec = 02◦ 12 are strong background sources. The higher resolution map at 4.85 GHz (Fig. 4) confirms these findings, while
revealing three more background sources (RA = 01h 05m 15s ,
Dec = 02◦ 14 and RA = 01h 05m 12s, Dec = 02◦ 05 30 with an extension towards RA = 01h 04m 55s , Dec = 02◦ 04 being a weak,
though slightly polarized background source). The main radio emission from the galaxy comes from strong H ii regions,
whereas the rest of the galaxy remains radio-quiet. The map
of polarized intensity of IC 1613 (Fig. 5) shows only two faint
patches of emission in the northeastern and southern outskirts
of the galaxy. They are however most likely associated with the
background sources mentioned above.
To summarize, only 3 out of 12 sources (25%) are detected at
radio wavelengths. The failed attempts to detect dwarfs are not
due to the lower sensitivity level of their respective radio maps,
as illustrated in Fig. 6. They are simply intrinsically weaker than
the detected objects. This is not quite an unexpected result as
we analyse the volume complete sample of LG dIrrs, unaffected
by any selection bias. Although 75% dwarfs from our complete
sample are undetected, they still provide important information
on the processes of magnetic field generation. By comparing the
undetected and detected LG dwarfs and by relating them to other
dwarfs observed so far (see Introduction), we can statistically infer which properties of the galaxies influence the radio emission
and the generation of magnetic fields in dwarfs (see Sect. 5).
4.2. Magnetic field strengths
After determining the radio emission flux or at least its upper
limit for all 12 LG dwarfs, we can calculate either the magnetic field strength or its upper limit, respectively. We derive
the thermal contributions to the total radio fluxes mostly from
Hα total fluxes. The classical model of H ii regions by Caplan
& Deharveng (1986) provides an estimate of the radio thermal emission from Hα fluxes, which we apply to the data at
2.64 GHz. Extinction due to dust is low in these galaxies (Hunter
& Elmegreen 2004), therefore Hα clearly traces the bulk of
galactic star formation and can be used to estimate the SFRs
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
Table 3. Magnetic field estimates and physical parameters for our sample of LG dwarfs and comparison dwarfs.
Btota
μG
SFRb
M yr−1
H i massc
106 M
Total massd
106 M
S60 μm e
mJy
vrot f
km s−1
σv g
km s−1
Aquarius
GR 8
IC 1613
NGC 6822
WLM
IC 10
LGS 3
SagDIG
Sextans A
Sextans B
Leo A
Pegasus
<4.5 ± 1.2
<3.6 ± 0.9
2.8 ± 0.7
4.0 ± 1.0
<3.9 ± 0.9
9.7 ± 2.0
<4.0 ± 1.0
<4.1 ± 1.1
<3.1 ± 0.8
<2.8 ± 0.6
<4.4 ± 1.2
<3.7 ± 0.9
4.6 × 10−5
7.0 × 10−4
3.0 × 10−3
2.1 × 10−2
1.0 × 10−3
6.0 × 10−2
2.5 × 10−6
6.7 × 10−5
2.0 × 10−3
2.0 × 10−3
3.2 × 10−5
3.0 × 10−4
2.7
9.6
58
140
63
98
0.2
8.6
54
44
7.6
3.4
5.4
7.6
795
1640
150
1580
13
9.6
395
885
11
58
139
20
1420
47 600
320
31 200
75
94
503
246
90
55
13
21
37
51
23
47
18
14
33
38
18
17
6.6
11.0
8.5
8.0
8.0
8.0
9.0
7.5
8.0
18.0
9.3
8.6
LMC
SMC
NGC 4449
NGC 1569
4.3 ± 1.0
3.2 ± 1.0
9.3 ± 2.0
14 ± 3.0
2.6 × 10−1
4.6 × 10−2
4.7 × 10−1
3.2 × 10−1
500
420
2500
130
20 000
2400
70 000
297
8.29 × 107
7.45 × 106
36 000
54 400
72
60
40
42
14.1
25.0
20.0
21.3
Galaxy name
References. (a) this paper and for LMC – Gaensler et al. (2005), SMC – Mao et al. (2008), NGC 4449 – estimation based on 4.86 GHz data (Chyży
et al. 2000), NGC 1569 – Kepley et al. (2010); (b) Woo et al. (2008), if not available – Hunter & Elmegreen (2004), for Aquarius and LGS 3
estimated from infrared emission; (c) Woo et al. (2008); NGC 1569 – Still & Israel (2002); NGC 4449 – Hunter et al. (1999); (d) Mateo (1998);
(e)
IRAS (Helou & Walker 1995; Moshir et al. 1990); ( f ) estimated rotational velocity defined as the maximum of rotational velocity and 2 times
the galaxy velocity dispersion – Woo et al. (2008), for NGC 4449 – Valdez-Gutiérrez (2002); (g) velocity dispersion of ISM estimated from H i:
Mateo (1998); LMC – Prevot et al. (1989); SMC – Staveley-Smith et al. (1997); NGC 1569 – Stil & Israel (2002); for NGC 4449 – Hunter et al.
(1999).
IC 1613 Effelsberg 4.85 GHz PI+% B-vect on DSS blue
02 16
14
14
12
12
DECLINATION (J2000)
DECLINATION (J2000)
IC 1613 Effelsberg 4.85 GHz TP+PI B-vect on DSS blue
02 16
10
08
10
08
06
06
04
04
02
02
01 05 15
00
04 45
RIGHT ASCENSION (J2000)
30
01 05 15
00
04 45
RIGHT ASCENSION (J2000)
30
Fig. 4. The total power map of IC 1613 at 4.85 GHz with apparent
B-vectors of polarized intensity overlaid onto the DSS blue image. The
contours are at 3, 5, 8, 12, 16, 25, 40, 100, 200 × 0.3 mJy/b.a., and a
vector of 1 length corresponds to the polarized intensity of 0.3 mJy/b.a.
The map resolution is 2. 6. The beam size is shown in the bottom left
corner of the figure.
Fig. 5. The map of polarized intensity of IC 1613 at 4.85 GHz with
apparent B-vectors of polarization degree overlaid onto the DSS blue
image. The contours are at 3, 5, 8, 12, 16 × 0.05 mJy/b.a., and a vector
of 1 length corresponds to the polarization degree of 20%. The map
resolution is 2. 6. The beam size is shown in the bottom left corner of
the figure.
from simple linear scaling (i.e. Kennicutt 1998). These SFRs
taken from the available literature are given in Table 3. For
Aquarius and LGS 3, which are undetected in Hα, the SFR and
the expected radio thermal emission is derived from the infrared
emission (Kennicutt 1998). The thermal radio fluxes are subtracted from the total radio fluxes (or their upper limits) to yield
estimates of the synchrotron emission.
To compute the equipartition magnetic field strengths, we
employed the formulae given by Beck & Krause (2005) (see
Appendix for details). Since the presented calculations include
the total magnetic field and its component perpendicular to the
line of sight, as well as the pathlength through the medium, it is
required to take into account the geometries of the investigated
galaxies and the contribution to the total field of both regular and
A94, page 5 of 15
A&A 529, A94 (2011)
3
5. Discussion
10
LMC
2
signal/rms
10
IC 10
SMC
NGC 6822
1
10
IC 1613
undetected
0
10
1
10
rms map noise [mJy]
Fig. 6. Signal to rms noise level ratio versus the noise level for our maps
of LG dwarfs and for maps of the Magellanic Clouds (Haynes et al.
1991) at 2.64 GHz. The undetected objects are marked.
As presented in Sect. 4.2, the magnetic fields in LG dwarfs
are statistically almost three times weaker than in typical spiral galaxies of various kinds. To estimate the influence of the
star formation rate and other galactic properties on the magnetic field production, we compiled various characteristics of our
dwarfs available in the literature. Table 3 includes global SFRs,
H i masses (MHI ), infrared fluxes at 60 μm, and rotational velocities of all dIrrs in our sample. Knowing the global SFR, we calculated the SFR surface density (ΣSFR) using object sizes from
Table 1. We obtained the gas surface density Σρ from the diskaveraged H i atomic gas. Since in dwarf galaxies, the molecular
gas contributes to the total gaseous mass only up to a few percent for the most massive objects (see e.g. Braine et al. 2001),
the atomic component closely represents the total gaseous mass
of dwarfs.
Below, we analyse various correlations of magnetic field
with other dwarf characteristics. For the sake of comparison we
also analyse four other well-known irregular dwarfs: both of the
Magellanic Clouds, NGC 1569, and NGC 4449.
5.1. Main factors regulating magnetic field
random components. As our aim is to search for the existence of
magnetic fields and estimate their upper limits, it is enough to assume ellipsoidal geometries for the studied galaxies, using their
minor axes as the synchrotron pathlength. To estimate the uncertainties in the estimated field strengths, we applied a variation in
all assumed parameters of 50%. Similar estimates of the magnetic field strengths were obtained at 4.85 GHz for galaxies detected at this frequency. They give values within the uncertainty
range of the strengths derived from the 2.64 GHz data.
For comparison, Table 3 also presents data for the LMC and
SMC dIrrs, which are also LG members but are situated in the
southern sky (thus not included in our unbiased LG sample). We
also present data for NGC 1569 and NGC 4449, dIrrs not belonging to the LG but with significant magnetic fields. NGC 1569 is
a nearby dwarf galaxy that experienced a very strong starburst
more than about 4 million years ago and now displays outflows
of hot metal-rich gas (Martin et al. 2002). NGC 4449 is an irregular starburst galaxy, which at optical wavelengths has properties similar to the Lyman-break galaxies (LBG) at high redshift
(Annibali et al. 2008).
The mean equipartition magnetic field strengths for our sample of LG dwarfs is <4.2 ± 1.8 μG, including the upper limits of
the field strength for the radio-undetected dwarfs at 2.64 GHz
(Table 3). The typical magnetic fields in dwarfs are thus significantly weaker than in spiral galaxies, for which the mean
field strength is about 10 μG (Beck 2005). In our LG sample, the
strongest field is observed in the starburst dwarf IC 10 and its
value of 9.7 μG is close to the that of starburst dIrrs (NGC 1569
and NGC 4449) from outside of the LG. Both Magellanic Clouds
have magnetic fields close to the estimated mean value for our
LG sample.
We also estimated the strength of the ordered magnetic field
of the LG dwarfs for which polarized emission was detected at
4.85 GHz (4.5 ± 0.5, 5.1 ± 2.1, and 0.10 ± 0.04 mJy for IC 10,
NGC 6822, and IC 1613, respectively). The strengths are in the
range of 0.4−0.9 μG. The ordered-to-random field ratio of those
galaxies is as large as about 0.2, which is similar to the averaged
field order in spiral galaxies. For undetected dwarfs, we expect
the production of an ordered field to be of the same efficiency or
lower.
A94, page 6 of 15
We determined mutual correlations between a range of parameters: magnetic field strength B, SFR, ΣSFR, MHI , Σρ, and the
dwarf’s unprojected linear size L, taken as the source major axis
from Table 1. Where possible, we included in the calculations
all 16 dwarfs, including the comparison dwarfs. When searching
for correlations with the magnetic field strength, we restricted
our calculations to radio-detected dIrrs (seven objects). Owing
to small number statistics, we chose to evaluate the Pearson correlation coefficient r and in each case performed a test of its
statistical significance. We determined the significance level as
the probability of rejecting a hypothesis that r = 0. Results are
presented in Table 4. In a similar way, we also performed analogous calculations for the Kendal rank correlation coefficients.
This approach led to the same following conclusions.
We found that among the various relations studied the magnetic field strength depends primarily on the density of the star
formation rate ΣSFR having the largest correlation coefficient
r = 0.94 (significant at the P = 0.2% level). This strong dependence can be intuitively understood because the local SFR determines the population of supernova explosions, which constitute
the main source of the turbulent energy, which is in turn vital to
the dynamo process (Arshakian et al. 2009, see also Sect. 5.4).
This relation shown in Fig. 7a can be quantified by the power-law
fit B ∝ ΣSFR0.30 ± 0.04 . A similar nonlinear relation between total
magnetic field strength and the global SFR has been observed for
nearby spiral galaxies (Krause 2009) and fits to the equipartition
model for the radio-FIR correlation (Niklas & Beck 1997). A
strong influence of the local SFR on the (random) magnetic field
has also been observed within the disk of a large spiral galaxy
NGC 4254 (Chyży 2008).
The remaining group of radio-undetected dwarfs occupy
a common region in the B − ΣSFR plane. If detected, they
would possibly move down in this plane as their current positions represent only upper limits to the magnetic field strength.
Therefore, the population of undetected dwarfs would likely fulfil the power-law determined for the radio-detected dwarfs alone.
We give another argument for this prediction in Sect. 5.5. We
also notice a gap in Fig. 7a between dwarfs of weak and strong
magnetic fields. This may be evidence of a threshold in either
the dynamo action producing magnetic fields, or the SFR above
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
0
16.0
10
NGC 1569
a)
b)
NGC 1569
-1
10
IC 10
IC 10
NGC 4449
-2
ΣSFR [Mo yr kpc ]
8.0
NGC 4449
-2
10
B [μG]
-1
NGC 6822
Aquarius
Leo A
4.0
WLM
Pegasus
LGS 3
Sextans B
Pegasus
Sextans A
IC 1613
WLM
Aquarius
GR 8
Sag DIG
-4
SMC
Sextans A
IC 1613
GR 8
-3
10
LMC
NGC 6822
Sag DIG
LGS 3
Aquarius
SMC
LMC
10
Sextans B
Leo A
LGS 3
-5
2.0
-5
10
-4
-3
10
-2
10
-1
10
10
--1
-2
Σ SFR [Mo yr kpc ]
10
0
1
10
2
10
6
-2
Σρ [10 Mo kpc ]
10
0
16.0
10
c)
d)
NGC 1569
NGC 4449
NGC 1569
LMC
-1
10
IC 10
IC 10
SMC
NGC 4449
NGC 6822
-2
8.0
IC 1613
B [μG]
-1
SFR [Mo yr ]
10
Aquarius
LMC
Leo A
LGS 3
4.0
NGC 6822
Sag DIG
GR 8
Sextans B
-3
GR 8
10
Sextans A
WLM
Pegasus
-4
10
WLM
Pegasus
Aquarius
SMC
Sag DIG
Leo A
Sextans A
Sextans B
IC 1613
-3
-2
-5
10
LGS 3
2.0
-6
10
-6
-5
10
-4
10
10
-1
SFR [Mo yr ]
10
10
-1
10
-1
10
0
10
1
10
2
10
6
MHI [10 Mo]
3
10
4
10
Fig. 7. Correlations of the magnetic field strength and SFR with other parameters. LG dwarfs from our sample, LMC, and SMC are marked by
circles or in cases when the upper limit of the radio emission was applied – by triangles. Comparison dwarfs are marked by squares. The solid
lines present power-law fits. Fits a and c are restricted to radio-detected dwarfs only (circles and squares).
Table 4. Correlation coefficients, their significance levels in percentages, and the number of dwarfs included in calculations.
SFR
ΣSFR
MHI
Σρ
L
ΣSFR
0.90 (0.001%;16)
−
−
−
−
MHI
0.93 (0.001%;16)
0.72 (0.2%;16)
−
−
−
Σρ
0.65 (1%;16)
0.77 (0.001%;16)
0.66 (1%,16)
−
−
which (ΣSFR ≈ 10−2 M yr−1 kpc−2 ) the dynamo activity is enhanced.
The physical processes underlying both the star formation
and magnetic fields in our sample of dwarfs are usually modelled by relating the surface density of galactic SFR (ΣSFR) to
the gas surface density Σρ (Kennicutt 1998). The empirical fit
to a power-law relation ΣSFR ∝ ΣρN with N ≈ 1.4 was found
to provide an appropriate parametrization of these processes for
different types of galaxies (Schmidt 1959). It follows that the gas
density is a major factor influencing the star formation rate. We
find that our dwarf galaxies also follow a similar power-law fit
(Fig. 7a, Table 4) with a slope of N = 1.83 ± 0.30 and a correlation of r = 0.77 (which is significant at much less than the
P = 1% level). The slope is somewhat steeper but agrees within
its broad uncertainty limits with the aforementioned Schmidt
law. The slightly steeper relation found for dwarfs, which are
relatively low-mass objects, is also reasonable, as some starformation thresholds in low-density (low-mass) galaxies are
L
0.82 (0.01%;16)
0.50 (5%;16)
0.92 (0.001%:16)
0.33 (21%:16)
−
B
0.70 (8%;7)
0.94 (0.2%;7)
0.16 (73%;7)
0.78 (4%;7)
−0.36 (43%,7)
expected (Kennicutt 1998). It is also likely that the Schmidt law
is a strong oversimplification as H i gas is only a weak tracer of
star formation, and even CO gas has a too low excitation temperature to serve as a good star formation tracer. Hence, a significant
fraction of the gas is unrelated to star formation, explaining the
loose correlation shown in Fig. 7b.
The ΣSFR – Σρ relation observed for our dwarfs causes in
turn a significant correlation for the gas density and the magnetic field strength (Table 4). Hence, in contrast to the B − ΣSFR
relation, we can also describe the magnetic field in dwarfs as
being controlled by the local gas density. For the radio-detected
dwarfs, we obtained the relationship of B ∝ Σρ0.47 ± 0.09 with a
correlation of r = +0.78 (P = 4%). This relation is very close
to that determined for spiral and irregular galaxies by Niklas &
Beck (1997), who found an exponent of 0.48 ± 0.05.
It was shown that for a wide range of galaxies the far-infrared
luminosity is a linear indicator of the SFR (Kennicutt 1998).
Thus, to test this relation for dwarfs we can estimate ΣSFR for all
A94, page 7 of 15
A&A 529, A94 (2011)
A94, page 8 of 15
16.0
NGC 1569
IC 10
NGC 4449
8.0
B [μG]
investigated dwarfs independently of the Hα emission using the
available infrared 60 μm fluxes (Table 3). After determining the
dependence of gas density on star formation (exponent 1.83) and
the relation of magnetic field to gas density (exponent 0.47), we
can model the relation between magnetic field and the surfacenormalized infrared luminosity of B ∝ ΣL0.26
IR . The observed relation for radio-detected dwarfs gives a power-law fit with the
exponent of 0.25 ± 0.04 (correlation r = +0.90, P = 0.5%),
which is in a good agreement with the predicted one. We also
found that this relation is compatible with the one determined for
the ΣSFR estimated in a similar way from Hα emission (with the
slope 0.30 ± 0.04). In summary, we can state that in dwarf galaxies the gas density regulates both the star-formation rate and the
magnetic field production in a way similar to the spiral galaxies (Krause 2009) and the late-type galaxies (Chyży et al. 2007)
studied so far.
We also found that the magnetic field is stronger in dIrrs
of higher global SFR (Fig. 7c). This trend for the seven
radio-detected dwarfs can be quantified by the relation B ∝
S FR0.25 ± 0.06 with the correlation coefficient of r = +0.70 (P =
8%). A similar relation with an exponent of 0.34 ± 0.08 was
fitted for the spiral galaxies by Niklas & Beck (1997), while
Vallée (2004) obtained an exponent of 0.13 ± 0.04 for a different
sample of nearby spirals. In our estimate, the exponent could
be just a lower limit, as we took into consideration only the
radio-detected (hence possibly relatively brighter) dwarfs (see
Fig. 7c). The correlation found between the global SFR and B
must involve some additional factors, not accounted for by the
local B − ΣSFR dependency discussed above (Fig. 7b).
One possible explanation of the B − S FR relation could be
the galactic mass. According to the principal component analysis of various global characteristics of galaxies performed by
Disney et al. (2008), the galactic mass is the principal component
strongly affecting a wide range of other global galactic properties. Plotted together, the H i mass and SFR of dwarfs are nonlineary related by a power-law slope of 1.45 ± 0.11 (r = +93,
P 1%, Fig. 7d). However, we do not observe a statistically
significant influence of the mass on magnetic field strengths in
dwarfs (r = +0.16, P = 73%). A larger sample of radio-detected
dwarfs is certainly needed to confirm this finding at higher statistical confidence.
If star formation in LG dwarfs were also a driver of effective galactic winds (see Sect. 5.3), then one might expect
weaker magnetic fields in actively star-forming dwarfs because
the fields and CRs could just escape in galactic outflows. To
check this idea, we compare the strength of the magnetic field
B with the velocity dispersion σv of ISM, which should scale
with the star formation activity. In the case of effective winds,
larger velocity dispersion should correspond to weaker fields.
We present the values of σv estimated from H i observations
in Table 3, and the derived B − σv relation in Figure 8. The
dIrrs with starbursts (NGC 1569, NGC 4449) have large velocity dispersions (σv > 20 km s−1 ) but also have strong magnetic
fields (B > 10 μG). The larger σv of both these galaxies and
the Magellanic Clouds could be caused by galactic winds and/or
by specific gas motions due to their tidal interactions. For dIrrs
with weak magnetic fields (B < 5 μG), the velocity dispersion is
around 10 ± 2 km−1 , which is a value typically found in quiescent galaxies. Therefore, to explain the B − σv relation of dIrrs,
galactic outflows are not needed, hence we ascribe the presence
of weak magnetic fields to low star formation and not to galactic
winds.
A possible process that could also influence both the SFR
and magnetic fields is the gravitational interaction of galaxies.
Pegasus
Aquarius
Leo A
Sag DIG
4.0
NGC 6822
LMC
LGS 3
GR 8
Sextans A
WLM
SMC
IC 1613
Sextans B
2.0
6
12
-1
σv [km s ]
24
Fig. 8. Magnetic field strength versus velocity dispersion for dwarf
galaxies. See Fig. 7 for symbol coding.
Young et al. (1996) found that the efficiency of star formation
in interacting galaxies is significantly higher than in isolated objects. For the analysed dIrrs, clear signs of gravitational perturbations or gas infall were clearly detected in all most-intensively
star-forming objects: NGC 4449, NGC 1569, IC 10, LMC, and
SMC (see Table 3). Therefore, in dIrrs gravitational interactions can indeed stimulate massive star formation and promote
stronger magnetic fields in a way similar to that observed in the
Antennae galaxies (Chyży & Beck 2004). A larger sample of radio detected dIrrs is again necessary to confirm this possibility.
5.2. SFR evolution
The magnetic field in dIrrs, as in normal spiral galaxies, could
be related not only to the current state of star-forming activity, as
discussed above, but also to their recent star formation history.
The production of magnetic fields might then be connected to
the galaxy past. The evolution of global star formation can be
qualitatively studied in a plane of two dimensionless parameters,
p = log(SFR T 0 /LB ) and f = log[MHI /(SFR T 0 )], where LB
denotes the total blue luminosity of a galaxy and T 0 = 13.7 Gyr
the age of the Universe. The former parameter (p) characterizes
the past, and the latter ( f ) the future of the galactic star formation
(see Karachentsev & Kaisin 2007 for details). We calculated the
values of LB for dwarfs from the absolute B-magnitude given in
Mateo (1998) or, if unavailable, from the LEDA database. The
other parameters needed are given in Table 3. We found that the
investigated LG dIrrs show a similar distribution across the p − f
plane (Fig. 9) to the group of dwarf galaxies around the giant
spiral M 81 (Fig. 4 in Karachentsev & Kaisin 2007), thus seem
to be representative of our nearby region of the Universe.
The majority of all dwarfs with detectable radio emission
and magnetic fields are located in the bottom-right quarter of this
plane (Fig. 9). Despite being more massive objects, they produce
stars so efficiently, that their H i gas would be sufficient for just a
short period of time, e.g. for 10% of the Hubble time ( f ≈ −1.0)
for LMC and IC 10. The most extreme case among all dwarfs
is the starburst NGC 1569 with f = −1.5. Its star formation,
and accordingly also the production of a magnetic field, should
cease soon (the current level of SFR may continue only for the
next 400 Myr). Galaxies such as NGC 1569 are presumably at
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
amount of H i gas places this galaxy closer to the center of the
p − f plane than other starburst dwarfs. In the past, the galaxy
most likely acquired some gas from an interaction or possibly
a merger, as its inner part is counter-rotating with respect to
the outer envelope (Hunter et al. 1998). The strong and regular
magnetic field of NGC 4449 (almost 10 μG) is therefore likely
connected to the star formation history, star-formation triggering mechanisms, the acquired mass, and the entire complicated
history of the galaxy. The omission of these processes could
have prevented a fully successful numerical MHD modelling of
this object (Otmianowska-Mazur et al. 2000). This example also
shows that dIrrs do not seem to be simple galaxy systems, nor
easier to model than typical spiral galaxies.
Leo A
1
Sag DIG
f = log[MHI/(SFR)T0]
LGS 3
Aquarius
WLM
Sextans A
Sextans B
IC 1613
0
GR 8
Pegasus
SMC
NGC 6822
NGC 4449
LMC
-1
IC 10
NGC 1569
-1
0
p = log[(SFR)T0/LB]
1
Fig. 9. Dwarf galaxies on the past-future evolution plane: p =
log(S FR T 0 /L B ) and f = log[MHI /(S FR T 0 )]. The comparison galaxies from outside of the Local Group are shown by squares.
their major star-forming phase (large p value of 1.5), thus
might be analogs of starbursting (“young”) objects of the early
Universe. This conclusion is supported by an analysis of the star
formation history of NGC 1569 derived from a synthetic colormagnitude diagram method incorporating strong episodes of star
formation over the past Gyr (Angeretti et al. 2005). Within our
unbiased LG sample the only similar dwarf is IC 10 (p ≈ +0.5)
with strong magnetic fields of 9.7 μ G. The LMC is located at a
similar location in the p − f diagram. Its star-formation episodes
are believed to be triggered by close encounters with the Milky
Way over the past 4 Gyr (Bekki & Chiba 2005).
In contrast to the aforementioned bottom-right quarter, the
top-left quarter of the p − f plane is occupied by less evolved objects with a relatively weak star-formation activity (negative p)
that evolve slowly, despite having enough gas to produce stars.
Galaxies such as WLM, Sag DIG, Aquarius, LGS 3, and Leo A
( f ≥ 0.5) could even make stars for at least three times the
Hubble time with the current SFR. These galaxies are most common among the LG dwarfs and all lack any detectable magnetic
field. Thus, the existence of detectable magnetic fields in dwarfs
is not coincidental but connected to the whole galaxy evolution.
To check whether the magnetic properties of dwarfs are indeed related to their overall evolution we investigated the relation of magnetic field strength to the mean metallicity (12+O/H)
of the dwarfs, which we obtained for all the objects from the
compilation of Mateo (1998) and Braine et al. (2001). We
found that strong magnetic fields are observed exclusively in
the evolved systems of relatively high metallicity. No object
of metallicity 12+O/H < 8.1 has a magnetic field stronger than
5 μG, which indicates that the magnetic field production in
dwarfs is tightly connected to the galactic gas consumption during their lives. Since the metallicity of dwarfs strongly correlates
with their masses (Braine et al. 2001), this can explain the complex and mutual relation of magnetic field strength, global SFR,
and mass (Sect. 5.1).
A good example to illustrate these complex issues is the
well-studied NGC 4449. It shows a global starburst with a
widespread star-formation activity. It forms stars twice as rapidly
as the LMC, even though sizes of both galaxies are similar
(Table 3). NGC 4449 is also unusual in having neutral hydrogen gas extending to six times its Holmberg radius. The large
5.3. Magnetization of the IGM
The magnetic field strength defines statistical scaling relations
with other properties of LG dwarfs, such as ΣSFR, Σρ, and mass
(Sect. 5.1). Similar trends can also be observed for local regions within large spiral galaxies (Chyży 2008), indicating in
both cases some universal connections between various physical
mechanisms. Close links between the global stellar and dynamical properties of dwarfs were also observed by Woo et al. (2008)
and modelled for higher-redshift dwarfs by Tassis et al. (2008).
We therefore infer that the magnetic properties of LG dwarfs
can tell us something about magnetic fields in dwarf galaxies
in past cosmological epochs, in particular about the role they
might have played in magnetizing the intergalactic medium in
the early Universe. Low-mass galaxies with a weak gravitational
potential seem to be good candidates to support this process.
We perform below a straightforward modelling of whether dwarf
galaxies could actually be an efficient supplier of magnetic fields
to the IGM. We use the available data concerning the magnetic
field characteristics of the low-mass galactic systems that we observed within the Local Group and our current knowledge of
protogalaxies and their environments.
According to theoretical considerations, very weak seed
magnetic fields of the order of 10−20 −10−18 G could have
been generated in early cosmological epochs by a number
of mechanisms, including phase transitions, the Weibel instability (Medvedev & Loeb 1999), and the Biermann battery
(Widrow 2002; Zweibel 2006). Alternatively, seed fields could
have been produced by the first stars and amplified by dynamo processes in protogalaxies. The small-scale galactic dynamo could produce strong magnetic fields on timescales of
even 107 yr (Brandenburg & Subramanian 2005; Arshakian
et al. 2009). Outflows from protogalaxies could then seed the
IGM and massive galaxies that assembled at lower redshifts
with magnetic fields (Kronberg et al. 2001; Bertone et al. 2006;
Donnert et al. 2009; Kronberg et al. 1999; Samui et al. 2009;
Dubois & Teyssier 2010). Measurements of integrated Faraday
rotation of distant quasars as well as the modelling of the cosmological evolution of the IGM provide hints of a possible significant magnetization of the IGM at z ≈ 4−7 (Kronberg 2006).
On the other hand, the observations of Ly-α quasar absorption lines indicate that metals are present in the IGM up to
z ≈ 5 (Cowie et al. 1995; Songaila & Cowie 1996; Ellison
et al. 2000; Bouché at al. 2007). Various estimates suggest that
clouds obscuring quasars are located 200–500 kpc from protogalaxies (Meiksin 2009, and references therein). To transport
metals into these regions, some mechanisms, such as stellar
winds, supernova-driven galactic outflows, or AGN induced outflows, must be at work there. The same galactic outflows that
A94, page 9 of 15
A&A 529, A94 (2011)
Table 5. Modelling of the magnetization of the IGM.
Type
SF Mass
Redshift z
Wind energy Ew [erg]
SF size R0 [kpc]
Stall radius Rs [kpc]
B0 [G]
Bs [G]
Type
SFR
Redshift z
Wind energy Ew [erg]
SF size R0 [kpc]
Stall radius Rs [kpc]
B0 [G]
Bs [G]
Pri dSph Pri dIrr
LBG
LBG
instantaneous star formation
2.0e5
1.0e7
4.0e8
4.0e9
8
7
5
3
4.0e54
2.0e56
8.0e57
8.0e58
0.2
0.7
1.0
2.0
9
36
163
528
1.0e-6
1.0e-5
2.3e-5
4.0e-5
5.3e-10
1.9e-9
8.6e-10 5.7e-10
Local Group dIrrs
continuous SF
0.00001
0.0003
0.01
0.1
0
0
0
0
3.0e50
1.5e52
3.0e53
3.0e54
0.05
0.2
0.4
0.7
0.2
0.9
2.3
5.0
5.0e-7
1.0e-6
3.0e-6
8.0e-6
2.3e-8
5.5e-8
8.8e-8
1.5e-7
Notes. From the assumed values of redshift z, T IGM , , R0 , B0 , SF mass
or SFR, we first model Ew by the Starburst99 code and next obtain Rs
and Bs (see the text for details).
pollute the space with metals could also supply the IGM with
magnetic fields produced in protogalaxies.
In our modelling, we study a galactic-wind-blown bubble which energy Eb drives the bubble expansion (Veilleux
et al. 2005; Meiksin 2009). Only some net fraction of the injected energy Ew from supernovae and stellar winds is available
for this process (Eb = Ew ), which can only be roughly estimated to be within 0.01−0.1, as it depends on several unknown
factors such as: expansion losses, wind mass loading, radiative
cooling, uniformity of the ambient medium, and energy losses
intrinsic to the interstellar medium (e.g. Bertone et al. 2006; Cho
& Kang 2008; Meiksin 2009). The bubble of radius Rb and thermal pressure Pb = Eb /2πR3b finally reaches an equilibrium with
the IGM pressure PIGM ∝ T IGM (1 + z)3 and stops expanding at
the stall radius Rs = (Eb /T IGM )1/3 (1 + z)−1 .
Next, we assume that magnetic fields are also blown out
along with the plasma that has escaped from star forming regions
and reached the strength Bs at radius Rs . For spherical expansion of the bubble, the strength of the magnetic fields dominated
by the random component scales with the bubble’s density as
Bb ∝ ρ2/3 . Following the results of Sect. 5.1, we relate the initial
strength of the magnetic fields B0 within a star forming region
of extent R0 to the total galactic mass and the global SFR, using
masses and sizes of the protogalaxies estimated from observations (see below) (Table 5).
We calculated the amount of mechanical energy Ew injected
by active star-forming regions by modelling an evolutionary stellar population synthesis using the Starburst99 code3 (Leitherer
et al. 1999; Vazquez & Leitherer 2005). The main input parameter of this code is the star forming (SF) mass in the case of instantaneous star formation, or the SFR in the case of continuous
star formation. For high-z objects, we used the former option to
simulate the burst of star formation during the formation process
of primordial galaxies, as well as the enhanced Geneva stellar
tracks of low metallicity Z = 0.004, appropriate for young galaxies. For the stellar initial mass function, the classical Salpeter law
was used in-between 1 and 100 M .
3
The code used is the latest version 5.1 (April 2006).
A94, page 10 of 15
According to the CDM scenario, the first dark matter halos appeared in the Universe at z ≈ 20−8. The observational
characteristics of dSphs in the LG (see Sect. 2), which have
the common total mass of about 107 M (Strigari et al. 2008),
suggest that they may constitute LG fossils of primordial dSph
(Pri dSph) galaxies (Ricotti 2010). Almost all LG dSphs exhibit
a prominent stellar population of about 10 Gyr in age, resulting from a SFR of about several hundred M per Myr (Dolphin
et al. 2005) followed by a subsequent decline in SF activity. The
lower-mass galaxies, which fossils can now be observed as UF
dSphs, were less efficient in forming stars and transformed a
smaller fraction of their baryonic mass into stars (Salvadori &
Ferrara 2009). In our modelling, we therefore restricted the lowend of the instantaneous SF mass to 2 × 105 M (Table 5). For a
total galactic mass of dSphs of e.g., several 107 M , this corresponds to 14% of the baryonic content, converting 3.5% of the
gas into stars in a single outburst. The applied values of SF mass
correspond to a mean SFR of 5 × 10−3 M yr−1 over the time of
the starburst (≈4 × 107 yr), which is close to the SFR estimated
by Dolphin et al. (2005) and several orders of magnitude higher
than the SFR observed today among LG dSphs. They are also
similar to those used in simulations of dwarf galaxy evolution
by Ricotti et al. (2008, 2010).
Low-mass systems might have merged in the past to form
larger galaxies, as predicted by the model of hierarchical cosmology. The primordial dwarf irregular galaxies (Pri dIrr) probably formed later than Pri dSphs or in more massive halos (Ricotti
& Gnedin 2005). In our modelling, we assigned them a SF
mass of 107 M (Table 5). This value corresponds to the case
of a strong burst of star formation of about 0.3 M yr−1 that
can be observed currently in the starbursting dwarf NGC 1569
(Table 3). This galaxy was much quieter in the past, including
its youth (Angeretti et al. 2005). Most LG dIrrs probably experienced less massive bursts of star formation during their evolution. For example, the SFR mentioned above is two orders of
magnitude higher than the current SFR of IC 1613 (Table 3) and
about one order of magnitude higher than during the most active
stage in the whole evolution of this object (Skillman et al. 2003).
More massive and starbursting galaxies have been detected
as Lyman-break galaxies (LBGs) (Verma et al. 2007). These objects are probably progenitors of the present-day early Hubbletype galaxies and bulges of massive galaxies. LBGs evolved with
time in mass: those assembled at z ≈ 5 are 10 times less massive and luminous than z ≈ 3 LBGs (Verma et al. 2007). Our
modelling includes both types of LBGs (at z = 5 and z = 3)
as the high-end mass systems (Table 5). The applied SF masses
(4 × 108 and 4 × 108 M ) correspond to an equivalent SFR during the starburst of 10 and 100 M yr−1 , respectively. Thus, the
second class of LBGs corresponds in terms of their properties to
the M 82-like starburst galaxies. In galaxies with masses significantly higher than 109 M , the escape of gas from the galactic
disks becomes problematic because of the deep gravitational potential wells (Ferrara & Tolstoy 2000). Therefore, the modelled
Rs for LBGs at z = 3 should be regarded as upper limits. We
also note that sometimes even relatively massive galaxies with
a total mass of up to ≈1011 M are called dwarf galaxies (e.g.
Crain et al. 2009) in the sense that they have a sub-galactic mass
value compared to the typical galactic systems in the present
Universe, such as the Milky Way. However, primordial systems
of this mass, as well as LBGs, would not have evolved to become
the typical LG dIrrs that we investigate in this paper.
For all kind of objects, we adopt in our modelling T IGM =
104 K (Meiksin 2009) and = 0.01, for which we get for
LBGs at z = 3 the bubble’s stall radius of Rs = 530 kpc
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
(Table 5), in agreement with the modelling of metal enrichment
by Madau et al. (2001), Calura & Matteucci (2006), and Samui
et al. (2008). Our modelling predicts a small stall radius of 9 kpc
for primordial dSphs and 36 kpc for primordial dIrrs (Table 5).
Thus, it is quite unlikely that the metal absorption systems seen
in the Ly-α forest out to at least 300 kpc from parent objects were
produced by low-mass dIrrs.
If these attempts to explain the IGM’s metal enrichment are
valid, our modelling indicates that the primordial dIrrs could
have magnetized the IGM only locally, out to about a 40 kpc
distance, with the strength of magnetic fields of about a few
nanogauss (Table 5). Accordingly, the contribution from these
galaxies is simply insufficient to have any significant impact on
magnetization of the IGM. Our modelling suggests that more
massive galaxies, such as LBGs, are more effective in magnetizing the IGM, providing a larger spread (160–530 kpc) and magnetic field strengths of almost one nanogauss. Kinematic signatures of vigorous large-scale winds have been detected among
LBGs at z ≈ 3−4 (e.g. Veilleux et al. 2005).
We now examine the effect of varying the model parameters.
Raising the energy conversion fraction from 0.01 (applied in
Table 5) to 0.1 doubles the bubble’s stall radius, while decreasing the magnetic field strength by factor of five. Thus, the applied = 0.01 results in upper limits of Bs presented in Table 5.
Extending the lower end of the Salpeter IMF to 0.1 M or raising its upper level to 120 M results in an input wind energy that
is lower by a factor of 2.5 and in turn, a 35% smaller Rs and
1.8 times stronger magnetic fields. If we decrease R0 by a factor
of two, we obtain a four times weaker magnetic field. Altering
the other input parameters has a less significant effect; for example, by changing the IMF to the standard Kroupa one decreases
the input energy by only 68%. Changing the metallicity from
0.004 to 0.02 gives a wind energy higher by 20%, a stall radius
larger by 7%, and a magnetic field strength lower by 15%. A
higher star-forming mass or lower IGM temperature by a factor
of two yield a stall radius larger by about 25% and a magnetic
field strength weaker by about 60%. This analysis demonstrates
that the obtained results are most sensitive to the uncertain value
of . However, even assuming that its uncertainty is as large as
about one order of magnitude does not affect our conclusion concerning the weak effectiveness of dwarf galaxies in polluting the
IGM with metals and magnetic fields.
We also perform similar modelling of spreading the magnetic fields of nearby (z = 0) dwarfs. As LG dIrrs appear to
experience continuous star formation with amplitude variations
of factors 2−3 during their lifetime (e.g. Grebel 2004, 2005), we
applied this option to our modelling of stellar population synthesis over a characteristic timescales of 107 yrs, and applied a
metallicity of Z = 0.02 (Table 5). Continuous star formation
agrees with the detection of significant amounts of gas in these
systems (Mateo 1998). We adopted a higher ambient gas temperature (T IGM = 105 K), as the IGM in the LG is not pristine and
likely to have a hot component due to galactic feedback, structure formation heating, and the large potential wells of massive
spirals (Davé & Oppenheimer 2007; Crain et al. 2009). There are
also some predictions that the density of the local IGM is about
10−4 cm−3 (Pildis & McGaugh 1996; Rasmussen et al. 2003;
Sembach 2006), which we use to estimate the ambient pressure
PIGM .
Our modelling indicates that typical LG dwarfs do not
appear capable of providing an efficient supply of magnetic
fields to their environments. Typical wind-blown expanding
bubbles may reach relatively short distances of about 1 kpc
(Table 5). Only around the most starbursting dwarfs (as e.g.
IC 10, NGC 1569, NGC 4449) could the IGM be magnetized in
this way up to about 0.1 μG and within a distance of about 2–
5 kpc.
In the above modelling, the galactic outflows were driven
exclusively by thermal pressure. However, the energy of CRs
may also play an important role in triggering galactic winds e.g.
Breitschwerdt et al. (1991, 1993), Breitschwerdt (2008), Everett
et al. (2008, 2010). This source of energy could be highly important in quiescent galaxies, such as our Milky Way (Everett
et al. 2010). Nevertheless, we attempt to estimate the possible
influence of additional pressure from CRs to blow-out bubbles
in our low-mass objects. Treating CRs hydrodynamically and
assuming that their pressure could reach approximate equipartition with the thermal pressure Pb , we repeated the modelling of
the expansion of the bubble for primordial dSphs and dIrrs. We
obtain stall radius of 11 and 45 kpc, respectively. These values
are only 26% larger than in the case of purely thermally driven
winds. These estimates seems to be upper limits as we do not
include any quenching effect of CRs on star formation (Socrates
et al. 2008; Samui et al. 2009) and the interaction of CRs with
mass-loaded gaseous outflows.
Thus, we conclude that it is highly unlikely that typical dwarf
galaxies (e.g. IC 1613) could have had any major role in magnetizing the Universe at any cosmological epoch. Our predictions
of the magnetized surroundings of nearby dIrrs should be verified by observations at very long radio wavelengths to possibly reveal an aged population of CR electrons radiating in weak
magnetic fields, or by Faraday rotation observations applied to
background sources. These possibilities are only now becoming
possible with the availability of the LOFAR and SKA pathfinders (Morganti et al. 2010; Beck 2010), as well as the EVLA.
5.4. Production of large-scale fields
We demonstrated that magnetic fields in the LG dIrrs (if detectable) are not more ordered than in typical spiral galaxies
(Sect. 4.2) and must be dominated by the random component.
This conclusion suggests that LG dwarfs might not fulfil the
evolutionary scenario of Arshakian et al. (2009) that local and
moderately distant (z ≈ 1) dwarfs can produce highly coherent
(unidirectional) fields.
The generation of coherent (regular) fields requires largescale dynamo process to operate, hence helical turbulence
produced by supernovae explosions and Coriolis forces
(Widrow 2002). The dynamo efficiency is approximately described by the dynamo number
D=9
H 2 Ω ∂Ω
,
r
∂r
v2t
which depends on the vertical scale height of the galactic disk
H, turbulent velocity vt , an angular rotation Ω, and the velocity
shear (r∂Ω/∂r). The large-scale α-Ω dynamo works only if D
exceeds a critical number of about 9-11, depending on the details of the gas flow pattern. For the LG dwarfs, we estimated
the maximum rotational velocities vrot from the galactic rotation
curves or velocity dispersions (see Table 3 with notes). As some
galaxies show evidence of gravitational interactions, these esimates are only approximate. For example, for strongly interacting NGC 4449 Valdez-Gutiérrez et al. (2002) estimate that the
systematic rotation on the receding side of the galaxy is about
40 km s−1 at 2 radius (from Hα measurements). On the same
portion of the galaxy, the H i observations indicate a rotation of
about 30 km s−1 (Martin 1998). The typical maximum rotational
A94, page 11 of 15
A&A 529, A94 (2011)
16.0
-1.0
NGC 1569
NGC 1569
NGC 4449
Surface brightness correlation
2.64 GHz and 60μm
IC 10
-2.0
B [μG]
8.0
4.0
LGS 3
log(I2.64GHz)
Pegasus
Aquarius
LMC
NGC 6822
Sag DIG
Leo A GR 8
WLM
SMC
Sextans A
LMC
-3.0
NGC 6822
GR 8
Aquarius
IC 1613
Sextans B
-4.0
2.0
1
10
NGC 4449
IC 10
SMC
LGS 3
Sag DIG
Leo A WLM Sextans B
NGC 3109
Pegasus
Sextans A
IC 1613
2
10
-1
Vrot [km s ]
Fig. 10. Total magnetic field strengths plotted against rotational velocities of dwarfs.
-5.0
-3.0
-2.0
−1
velocity for dwarfs is about 30 km s at a radius r = 2 kpc. For
differential rotation and flat rotation curve, this corresponds to
a shear of 15 km s−1 kpc−1 . Taking vt = 10 km s−1 , H = 0.5 kpc
(cf. Elstner et al. 2009), we obtain a dynamo number of D = 5,
which is subcritical and hence in agreement with our radio observations. If this rotation were not differential (e.g. more chaotic),
then D would be even smaller. This is confirmed by direct simulations of a supernova-driven dynamo by Gressel et al. (2008),
who did not find large-scale dynamo action within a galactic disk
of corresponding shear 20 km s−1 kpc−1 . Recent MHD simulations of a cosmic-ray driven dynamo by Siejkowski et al. (2010)
show that the production of regular fields in dwarf galaxies requires mainly fast rotation. The velocity shear is necessary but
influences the dynamo efficiency much less.
In typical and even the most starbursting LG dwarf (IC 10),
the ordered magnetic fields have indeed been observed so far
not to show any large-scale structure that could resemble MHD
dynamo fields (Chyży et al. 2003). This confirms the earlier suggestion by Chyży et al. (2003) that small galaxies should mainly
produce random magnetic fields maintained by turbulent gas
motions. The large irregular dwarf NGC 4449 with its dynamolike field could be a special case (Sect. 5.2). Rotation in dwarfs
is usually not only slower but also more chaotic than in spiral
galaxies (e.g. van Eymeren et al. 2009). Larger velocity dispersion and star formation feedback may destroy the regular pattern
of magnetic fields and lower the field regularity. No MHD simulations have hitherto addressed these possibilities.
We do not observe a systematic dependence of the maximum rotational velocity on the total magnetic field strength
in dwarfs (Fig. 10). For slow rotation (vrot < 40 km s−1 ), all
dwarf galaxies show weak fields (B < 4 μG). Above a velocity
of 40 km s−1 , dwarfs have either stronger or weaker fields that
seems to mainly depend on the actual value of the SFR. Indeed,
NGC 6822, LMC, and SMC rotate at least as fast as the starbursting galaxies IC 10, NGC 1569, and NGC 4449, but they have less
active and widespread star formation.
According to a study of magnetic fields within the disk of the
large spiral galaxy NGC 4254 (Chyży 2008), the random magnetic field scales with the far-infrared based ΣSFR as a powerlaw
with an exponent of 0.26 ± 0.01. A similar relation with exponent of 0.25 ± 0.04 has also been found for LG dIrrs (Sect. 5.1).
We are currently collecting data on galaxies with properties inbetween those of the dwarfs studied in this paper and spiral
galaxies to confirm these findings for a larger sample of galaxies.
A94, page 12 of 15
-1.0
log(I60μm)
0.0
1.0
Fig. 11. The radio-infrared correlation diagram for LG dwarfs and comparison dwarfs (plotted with the same symbols as in Fig. 7), and for the
sake of reference, the sample of galaxies observed by de Jong (1967)
plotted as stars. The surface brightness at 2.64 GHz and at 60 μm is used
(in Jy/
). The solid line is an orthogonal fit to the reference galaxies.
5.5. Radio-infrared relation
We constructed for the first time a radio-infrared correlation diagram for dwarf galaxies (Fig. 11), extending this relation to the
lowest limit of galactic mass of about several 107 M , which
is 10 times lower than previously studied (Chyży et al. 2007).
We used the surface brightness radio emission at 2.64 GHz (or
its limits) and the infrared surface brightness emission at 60 μm
(Table 3). The relation for detected dwarfs is closely represented
by the powerlaw with a slope of 0.91 ± 0.08 and a correlation of
r = +0.91 (P 1%) determined for a sample of bright galaxies
observed by de Jong (1967) with the 100 m NRAO telescope.
Hence, typically unevolved, low-mass stellar systems in our local neighbourhood reveal similar physical conditions for star formation, magnetic field, and cosmic-ray generation processes as
the massive spirals (e.g. Weżgowiec et al. 2007). A similar relation was extended to young, high-redshift galaxies (Seymour
et al. 2008).
However, it cannot be excluded that some radio deficiency
might be present in some dwarfs of weak infrared radiation,
as only the upper limits of their radio brightness are plotted in
Fig. 11. The loss of magnetic fields and CRs by galactic outflows in dwarfs and subsequently their weaker synchrotron emission could be counterbalanced by the lower content of dust as
suggested for blue compact dwarfs by Klein at al. (1991). In
this case, the radio-infrared relation could be preserved. Because
dIrrs at the low-end of the radio flux also have lower metallicity (which scales with the object’s mass) the shortage of dust is
indeed likely to occur.
According to the radio-infrared relation, the radioundetected dwarfs from our LG sample are expected to have
a radio brightness at 2.64 GHz of about 1 mJy per 1 beam
or less. This requires a few times higher detecting sensitivity
than we have achieved with the Effelsberg telescope. However,
these fluxes are below the confusion limit of a single-dish antenna and demand observations of higher resolution. Objects
with such weak and extended radio emission are extremely
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
difficult to detect at higher frequencies. Studies at lower frequencies would thus require a high-sensitivity radio interferometer
such as LOFAR. If these dwarf galaxies hosted primarily regular
magnetic fields of about 1 μG strength (Arshakian et al. 2009),
then they could also be detected by the background Faraday rotation method with the upcoming LOFAR or SKA interferometers.
6. Summary and conclusions
We have performed a sensitive search for radio emission in a
statistically unbiased sample of the Local Group irregular and
dwarf irregular galaxies available at the site of 100-m Effelsberg
telescope at 2.64 GHz. We have compared these 12 galaxies to
other LG objects, i.e., LMC and SMC, and the starburst dwarfs
NGC 4449 and NGC 1569, for which magnetic fields have already been observed. Higher frequency (4.85 GHz) observations
were used to search for polarized emission in the five most luminous dwarfs in the infrared domain.
We found the following:
– The LG dIrrs closely represent the local volume of the
Universe and display star-formation characteristics similar to
those of other nearby groups of dwarfs (Sect. 5.2). Only 25%
of the LG dwarfs (3 out of 12) were detected at 2.64 GHz. We
argued that the radio-undetected dwarfs must be intrinsically
radio weak.
– The total magnetic fields in LG dwarfs are very weak: the
mean value of the equipartition magnetic field strength of all
objects is <4.2 ± 1.8 μG, taking into account the upper limits
for radio-undetected dwarfs (9 out of 12). This value is almost three times weaker than the estimated mean for typical
spiral galaxies. The strongest total field of 10 μG is observed
in the starburst dwarf IC 10. We found that the magnetic field
strength does not correlate with the dwarf rotational velocity.
– Among the three radio-detected dwarfs, the strength of the
ordered field component is in the range 0.4−0.9 μG and the
ordered-to-random field component ratio is about 0.2. These
values are smaller than in typical spiral galaxies indicating
that the production of magnetic fields in dwarfs is probably
not maintained by the large-scale dynamo process.
– The production of the total magnetic field in dwarf systems appears to be controlled mainly by the star-formation
surface density (B ∝ ΣSFR0.30 ± 0.04 ), or the gas density
(B ∝ Σρ0.47 ± 0.09 ), as for spiral galaxies (Chyży 2008;
Krause 2009). We note a somewhat steeper Schmidt law (a
slope N = 1.8) for our LG dwarfs than in typical largemass disks. Among all the dwarfs, we also found systematically stronger magnetic fields in objects of higher global
SFR (B ∝ S FR0.25 ± 0.06 ).
– Stronger disk-averaged magnetic fields (>4 μG) were observed in dIrrs of extreme characteristics only (e.g.
NGC 4449, NGC 1569, and the LG dwarf IC 10). They are
more evolved objects of generally much higher metallicity
and global SFR than the majority of LG dwarf population.
They also usually show clear signs of current or recent gravitational interactions.
– We propose that a coeval magnetization of the IGM around
primordial galaxies occurs with a metal enrichment caused
by galactic outflows maintained by stellar winds and supernovae. However, our modelling of the stellar population synthesis (code Starburst99) and expansion of a blowing bubble indicate that not dIrrs but more massive galaxies of LBG
properties can efficiently magnetize the IGM at high (z > 3)
redshift. If the current understanding and modelling of metal
enrichment is valid, we expect that the most efficient seeding
of the IGM is that produced by LBG galaxies with magnetic
field strengths of about 0.9−0.6 nG at up to distances of 160–
530 kpc at redshifts 5–3, respectively. We show that several
times weaker fields and shorter distances are expected from
primordial dwarf galaxies.
– The sizes of blowing bubbles around primordial galaxies
might be slightly enlarged (by up to 26%) if in addition to
the thermal pressure the pressure of CRs is included.
– We also predict that around local, most star-forming dwarf
galaxies, the surrounding IGM is magnetized up to about
0.1 μG to within a distance of about 5 kpc. These predictions
should be verified by LOFAR, EVLA, and SKA observations.
– The dIrrs of different SFR follow the far-infrared relationship determined for high surface brightness spiral galaxies
(with a slope 0.91 ± 0.08), showing that similar processes
regulate star formation, synchrotron emission, and production of magnetic fields in low-mass dwarfs and large spirals.
From the radio-infrared relation, we predict for the radioundetected dwarfs in our sample a mean total field strength
as small as about 1 μG .
Acknowledgements. We are grateful to Prof. M. Urbanik for permission
to present 4.85 GHz data of IC 1613 from our common observation in
2002, and to Dr M. Soida for valuable discussions. K.T. Chyży is grateful to Prof. Claus Leitherer for his help in the compilation and setup of
the Starburst99 code. We thank Dr. M. Krause for careful reading of the
manuscript and an anonymous referee for helpful comments and suggestions. This work was supported by the Polish Ministry of Science and
Higher Education, grant 2693/H03/2006/31, 3033/B/H03/2008/35, and from research funding from the European Community’s sixth Framework Programme
under RadioNet R113CT 2003 5058187. We acknowledge the use of the
HyperLeda (http://leda.univ-lyon1.fr) and NED (http://nedwww.
ipac.caltech.edu) databases.
Appendix A: Derivation of magnetic field strengths
According to the theory of synchrotron emission (e.g.
Pacholczyk 1970), the total synchrotron intensity and the degree of linear polarization obtained from our radio polarimetric
observations can be used to calculate the strengths of the total
(Btot ) and regular (Breg ) magnetic field. With the assumption of
equipartition between the energy densities of the magnetic field
and cosmic rays (εCR = εBtot = Btot /8π), the total magnetic field
is (Beck & Krause 2005)
⎤ 1
⎡
⎢⎢⎢ 4π(2αn + 1)(K0 + 1)In Ep1−2αn ( 2cν )αn ⎥⎥⎥ αn +3
1
⎥⎥⎥
Btot = ⎢⎢⎢⎣
,
(A.1)
⎦
(2αn − 1)c2 αn Lc3
where K0 is the constant ratio of proton to electron number densities, In is the nonthermal intensity, and αn is the mean synchrotron spectral index, L denotes the pathlength through the
synchrotron emitting medium, Ep is the proton rest energy, and
c1 is a constant defined as
c1 =
3e
= 6.2648 × 1018 erg−2 s−1 G−1 .
4πm3e c5
(A.2)
The constants c2 and c3 depend on the spectral index and the
inclination of the magnetic field, respectively
5
(3αn + 5)
1 (αn + 3 ) (3αn + 1)
c2 (αn ) = c3
Γ
×Γ
,
(A.3)
4 (αn + 1)
6
6
where c3 = (cos i)αn +1 . This is true for a region where the field is
totally regular and has a constant inclination i with respect to the
A94, page 13 of 15
A&A 529, A94 (2011)
Table A.1. The dependence of the total magnetic field (in μG) of
NGC 6822 on the synchrotron pathlength (L) and the proton-to-electron
ratio (K0 ).
Ko /L [kpc]
50
75
100
125
150
1
3.97
4.39
4.73
5.00
5.24
1.5
3.57
3.96
4.26
4.51
4.72
2
3.34
3.70
3.98
4.21
4.41
2.5
3.14
3.47
3.74
3.95
4.14
3
2.99
3.31
3.57
3.77
3.95
Notes. The original value is marked in boldface.
sky plane. If the synchrotron intensity is averaged over a large
volume (as in estimating the mean field strength), the value of c3
has to be replaced by its average over all occurring values of i.
For a totally turbulent field, one needs to use c3 = (2/3)(αn +1)/2 .
To estimate the strength of the regular magnetic field in the
sky plane, we can use the observed nonthermal degree of polarization (Segalovitz et al. 1976)
⎤−1
⎡
1
⎢⎢⎢
3γ + 3
(1 − q)π 2 Γ[(γ + 5)/4] ⎥⎥⎥
⎥⎦ ,
=
× ⎢⎣1 +
3γ + 7
2qΓ[(γ + 7)/4]F(i)
Pnth
where
F(i) =
1
2π
2π
(1 − sin2 i sin2 θ)(γ+1)/4 dθ.
(A.4)
(A.5)
0
In the above formulae, q2 /(1 + γ) = Breg /Bturb , γ = 2αn + 1, and
θ is the azimuthal angle.
In calculating magnetic field strengths, some uncertainties
can be introduced by assuming a proton-to-electron number density ratio, as well as a geometry for the galaxy. We assume
ellipsoidal geometries of the studied galaxies, using their minor axes as the synchrotron pathlength. An ellipsoidal approximation of the geometry of a dwarf galaxy was applied by
Chyży et al. (2003) to derive the magnetic field strength for
NGC 6822 from the 4.85 GHz data. To test the influence of these
parameters, we performed calculations of the magnetic field in
NGC 6822, varying Ko in the range of 50–150 and L in the range
of 1–3 kpc. The results are presented in Table A.1. The largest
deviation in our calculations was 32% (see Table A.1), while typically it did not exceed 15%. Therefore, varying these parameters
by 50%, as we also did for the nonthermal flux and the degree
of polarization, to calculate the global error in the magnetic field
strengths (see Sect. 4.2), provides us with errors that thoroughly
estimate the possible uncertainties. We also tested whether the
magnetic field strength depends on galaxy distance, thus on the
location within the Local Group with respect to the Milky Way.
For all LG dIrrs, the correlation coefficient r = −0.37 with
P = 23%, which means that the distance has no statistically significant influence.
References
Annibali, F., Aloisi, A., Mack, J., et al. 2008, AJ, 135, 1900
Angeretti, L., Tosi, M., Greggio, L., et al. 2005, AJ, 129, 2203
Arshakian, T. G., Beck, R., Krause, M., & Sokoloff, D. 2009, A&A, 494, 21
Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559
Beck, R. 2005, in Cosmic Magnetic Fields, ed. R. Wielebinski, & R. Beck
(Heidelberg: Springer), 41
Beck, R., 2010, in Wide Field Science and Technology for the Square Kilometre
Array, ed. S. A. Torchinsky, et al. (SKADS), 93
Beck, R., & Krause, M. 2005, Astron. Nachr., 326, 414
Bekki, K., & Chiba, M. 2005, MNRAS, 356, 680
A94, page 14 of 15
Bertone, S., Vogt, C., & Enßlin, T. 2006, MNRAS, 370, 319
Bouché, N., Lehnert, M. D., Aguirre, A., Péroux, C., & Bergeron, J. 2007,
MNRAS, 378, 525
Braine, J., Duc, P.-A., Lisenfeld, U., et al. 2001, A&A, 378, 51
Brandenburg, A., & Subramanian, K. 2005, Phys. Rep., 417, 1
Breitschwerdt, D. 2008, Nature, 452, 826
Breitschwerdt, D., McKenzie, J. F., & Völk, H. J. 1991, A&A, 245, 79
Breitschwerdt, D., McKenzie, J. F., & Völk, H. J. 1993, A&A, 269, 54
Calura, F., & Matteucci, F. 2006 MNRAS, 369, 465
Caplan, J., & Deharveng, L. 1986, A&A, 155, 297
Cho, H., & Kang, H. 2008, New A, 13, 163
Chyży, K. T. 2008, A&A, 482, 755
Chyży, K. T., & Beck, R. 2004, A&A, 417, 541
Chyży, K. T., Beck, R., Kohle, S., Klein, U., & Urbanik, M. 2000, A&A, 355,
128
Chyży, K. T., Knapik, J., Bomans, D. J., et al. 2003, A&A, 405, 513
Chyży, K. T., Bomans, D. J., Krause, M., et al. 2007, A&A, 462, 933
Condon, J. J. 1987, ApJS, 65, 485
Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693
Cowie, L. L., Songaila, A., Kim, T.-S., & Hu, E. M. 1995, AJ, 109, 1522
Crain, R. A., Theuns, T., Dalla Vecchia, C., et al. 2009, MNRAS, 399, 1773
Davé, R., & Oppenheimer, B. D. 2007, MNRAS, 374, 427
Disney, M. J., Romano, J. D., Garcia-Appadoo, D. A., et al. 2008, Nature, 455,
1082
Dolphin, A. E., Weisz, D. R., Skillman, E. D., & Holtzman, J. A. 2005
[arXiv:astro-ph/0506430]
Donnert, J., Dolag, K., Lesch, H., & Müller, E. 2009, MNRAS, 392, 1008
de Jong, M. L. 1967, ApJ, 150, 1
Dubois, Y., & Teyssier, R. 2010, A&A, 523, A72
Ellison, S. L., Songaila, A., Schaye, J., & Pettini, M. 2000, AJ, 120, 1175
Elstner, D., Gressel, O., & Rüdiger, G. 2009, in Cosmic Magnetic Fields: From
Planets, to Stars and Galaxies, ed. K. G. Strassmeier, et al., IAU Symp. 259,
467
Emerson, D. T., & Gräve, R. 1988, A&A, 190, 353
Emerson, D. T., Klein, U., & Haslam, C. G. T. 1979, A&A, 76, 92
Everett, J. E., Zweibel, E. G., Benjamin, R. A., et al. 2008, ApJ, 674, 258
Everett, J. E., Schiller, Q. G., & Zweibel, E. G. 2010, ApJ, 711, 13
Ferrara, A., & Tolstoy, E. 2000, MNRAS, 313, 291
Gaensler, B. M., Haverkorn, M., Staveley-Smith, L., et al. 2005, Sci, 307, 1610
Gressel, O., Elstner, D., Ziegler, U., & Rüdiger, G. 2008, A&A, 486, L35
Gioia, I. M., Gregorini, L., & Klein, U. 1982, A&A, 116, 164
Grebel, E. K. 2001, A&SSS, 277, 231
Grebel, E. K. 2004, Carnegie Observatories Astrophys. Series, 4, 234
Grebel, E. K. 2005, in Stellar astrophysics with the world’s largest telescopes,
AIP Conf. Proc., 752, 161
Grebel, E. K., Gallagher, J. S. III, & Harbeck, D. 2003, AJ, 125, 1926
Haslam, C. G. T. 1974, A&AS, 15, 333
Haynes, R. F., Klein, U., Wayte, S. R., et al. 1991, A&A, 252, 475
Hunter, D. A., 2002, in Modes of Star Formation and the Origin of Field
Populations, ed. E. K. Grebel, & W. Brandner, San Francisco, ASP Conf.
Proc., 285, 323
Hunter, D. A., & Gallagher, J. S., 1990, in NASA, Ames Research Center, The
Interstellar Medium in External Galaxies, 149
Hunter, D. A., & Elmegreen, B. G. 2004, AJ, 128, 2170
Hunter, D. A., Wilcots, E. M., van Woerden, H., Gallagher, J. S., & Kohle, S.
1998, ApJ, 495, L47
Hunter, D. A., van Woerden, H., & Gallagher, J. S. 1999, AJ, 118, 2184
Helou, G., & Walker, D. W. 1995, IRAS Small Scale Structure Catalog, Ver 1.00
Vizier Online Data Catalog: VII/73
Karachentsev, I. D. 2005, AJ, 129, 178
Karachentsev, I. D., & Kaisin, S. S. 2007, AJ, 133, 1883
Kennicutt, R. C. 1998, ApJ, 498, 541
Kepley, A. A., Mühle, S., Everett, J., et al. 2010, ApJ, 712, 536
Klein, U., & Gräve, R. 1986, A&A, 161, 155
Klein, U., Weiland, H., & Brinks, E. 1991, A&A, 246, 323
Kravtsov, A. 2010, Adv. Astron., 2010, 1
Krause, M. 2009, Rev. Mex. Astron. Astrofis., 36, 25
Kronberg, P. P. 2006, AN, 327, 517
Kronberg, P. P., Lesch, H., & Hopp, U. 1999, ApJ, 511, 56
Kronberg, P. P., Dufton, Q. W., Li, H., & Colgate, S. A. 2001, ApJ, 560, 178
Leitherer, C., Schaerer, D., Goldader, J. D., et al. 1999, ApJS, 123, 3
Madau, P., Ferrara, A., & Rees, M. J. 2001, ApJ, 555, 92
Mao, S. A., Gaensler, B. M., Stanimirović, S., et al. 2008, ApJ, 688, 1029
Martin, C. L. 1998, ApJ, 506, 222
Martin, C. L., Kobulnicky, H. A., & Heckman, T. M. 2002, ApJ, 574, 663
Martin, N. F., de Jong, J. T. A., & Rix, H.-W. 2008, ApJ, 684, 1075
Mateo, M. 1998, ARA&A, 36, 435
Medvedev, M. V., & Loeb, A. 1999, ApJ, 526, 697
K. T. Chyży et al.: Magnetic fields in Local Group dwarfs
Meiksin, A. A. 2009, Rev. Mod. Phys., 81, 1405
Morganti, R., Rottgering, H., Snellen, I., et al. 2010 [arXiv:1001.2384]
Morsi, H. W., & Reich, W. 1986, A&A, 163, 313
Moshir, M., Copan, G., Conrow, T., et al. 1990, IRAS Faint Source Catalogue,
version 2.0, Vizier Online Data Catalog, 2156, 0
Niklas, S., & Beck, R. 1997, A&A, 320, 54
Otmianowska-Mazur, K., Chyży, K. T., Soida, M., & von Linden, S. 2000, A&A,
359, 29
Pacholczyk, A. G. 1970, Radio Astrophysics: Nonthermal Processes in Galactic
and Extragalactic Sources, Series of Books in Astronomy and Astrophysics
(San Francisco, CA: Freeman)
Pildis, R. A., & McGaugh, S. S. 1996, ApJ, 470, L77
Prevot, L., Rousseau, J., & Martin, N. 1989, A&A, 225, 303
Rasmussen, A., Kahn, S. M., & Paerels, F. 2003, in The IGM/Galaxy
Connection: The Distribution of Baryons at z = 0, ed. J. L. Rosenberg, &
M. E. Putman (Dordrecht: Kluwer Academic Publishers), ASSL Conf. Proc.,
281, 109
Ricotti, M. 2010, Adv. Astron., 2010, 1
Ricotti, M., & Gnedin, N. Y. 2005, ApJ, 629, 259
Ricotti, M., Gnedin, N. Y., & Shull, J. M. 2008, ApJ, 685, 21
Salvadori, S., & Ferrara, A. 2009, MNRAS, 395, L6
Samui, S., Subramanian, K., & Srianand, R. 2008, MNRAS, 385, 783
Samui, S., Subramanian, K., & Srianand, R. 2010, MNRAS, 402, 2778
Schmidt, M. 1959, ApJ, 129, 243
Segalovitz, A., Shane, W. W., & de Bruyn, A. G. 1976, Nature, 264, 222
Sembach, K. R. 2006, in The Local Group as an astrophysical laboratory, Proc.
of the Space Telescope Science Institute Symposium Series, ed. M. Livio, &
T. M. Brown (Cambridge Univ. Press), 17, 86
Seymour, N., Dwelly, Y., Moss, D., et al. 2008, MNRAS, 386, 1695
Siejkowski, H., Soida, M., Otmianowska-Mazur, K., Hanasz, M., & Bomans, D.
J. 2010, A&A, 510, A97
Skillman, E. D., Tolstoy, E., Cole, A. A., et al. 2003, ApJ, 596, 253
Socrates, A., Davis, S. W., & Ramirez-Ruiz, E. 2008, ApJ, 687, 202
Songaila, A., & Cowie, L. L. 1996, AJ, 112, 335
Staveley-Smith, L, Sault, R. J., Hatzidimitriou, D., Kesteven, M. J., &
McConnell, D. 1997, MNRAS, 289, 225
Stil, J. M., & Israel, F. P. 2002, A&A, 392, 473
Strigari, L. E., Bullock, J. S., Kaplinghat, M., et al. 2008, Nature, 454, 1096
Tabatabaei, F. S., Krause, M., Fletcher, A., & Beck, R. 2008, A&A, 490, 1005
Tassis, K., Kravtsov, A. V., & Gnedin, N. Y. 2008, ApJ, 672, 888
Tolstoy, E., Hill, V., & Tosi, M. 2009, ARA&A, 47, 371
Valdez-Gutiérrez, M., Rosado, M., Puerari, I., et al. 2002, ApJ, 124, 3157
Vallée, J. P. 2004, New Astron. Rev., 48, 763
van Eymeren, J., Marcelin, M., Koribalski, B., et al. 2009, A&A, 493, 511
Vazquez, G. A., & Leitherer, C. 2005, ApJ, 621, 695
Veilleux, S., Cecil, G., & Bland-Hawthorn, J. 2005, ARA&A, 43, 769
Verma, A., Lehnert, M. D., Förster Schreiber, N. M., Bremer, M. N., & Douglas,
L. 2007, MNRAS, 377, 1024
Weżgowiec, M., Urbanik, M., Vollmer, B., et al. 2007, A&A, 471, 93
Widrow, L. M. 2002, Rev. Mod. Phys., 74, 775
Woo, J., Courteau, S., & Dekel, A. 2008, MNRAS, 390, 1453
Young, J. S., Allen, L., Kenney, J. D. P., Lesser, A., & Rownd, B. 1996, AJ, 112,
1903
Zeldovich, Y. B., Ruzmaikin, A. A., & Sokoloff, D. D. 1990, The Almighty
Chance (Singapore: World Scientific Publication)
Zweibel, E. G. 2006, Astron. Nachr., 327, 505
A94, page 15 of 15